For transmitting data in high speed, a Multi-Input, Multi-Output (MIMO) system which uses a plurality of antennas to transmit and receive data. If the number of base station antennas (M) is larger than the number of mobile station antennas (N), the amount of data that can be transmitted via the downlink MIMO channel is compared to N, and the base station (BS) transmits N number of data streams simultaneously, making it high speed transmission possible. In the MIMO system for a single user, if the BS has information on the status of the downlink channel, the BS uses a Singular Value Decomposition (SVD) scheme for beam forming to increase the amount of data that can be transmitted via a channel by the increase in Signal-to-Noise Ratio (SNR) and to achieve transmission gain from parallel data streams.
FIG. 1 is a diagram illustrating a Multi-Input, Multi-Output (MIM) system. In FIG. 1, the receiving end uses a channel matrix (H) to calculate a precoding matrix (W). The receiving end can then transmit directly the calculated W as feedback to the transmitting end. Alternatively, a multiple values corresponding to the calculated W can be defined or set in advance between the transmitting end and the receiving end. The receiving end can then send as feedback an index the predefined value closest or most similar to the calculated W value.
Most of the existing closed loop MIMO algorithm uses the SVD scheme. In other words, in determining W, the SVD is applied to HHH to acquire an Unitary Matrix (U), which is then used to replace W.
In addition, a signal vector (x) of the receiving end can be defined according to the following equation.x=HWs+v  [Equation 1]
In Equation 1, x represents a receiving signal vector, H represents a channel matrix, W represents a precoding matrix, s represents a transmission signal vector before being precoded, and v represents white noise.
The following Equation 2 denotes the SVD scheme applied to Equation 1.x=HUs+v  [Equation 2]
In Equation 2, U represents the Unitary Matrix acquired from applying the SVC to HHH (HH is a Hermitian operation of the H matrix).
Based on the characteristics of the Unitary Matrix and Equation 2, the following Equations 3-5 are formed.HHH=UΣUH  [Equation 3]
                    ∑                  =                      [                                                                                ∑                    1                    2                                                                    0                                                  0                                                  0                                                                              0                                                                      ∑                    2                    2                                                                    ⋯                                                  0                                                                              ⋮                                                  ⋮                                                  ⋱                                                  ⋮                                                                              0                                                  0                                                  ⋯                                                                      ∑                    N                    2                                                                        ]                                              [                  Equation          ⁢                                          ⁢          4                ]            UHU=I  [Equation 5]
At the same time, to attain a transmission signal vector s, the following equation is used.s=UHHHx=UHHHHUs+UHHHv=Σs+Σ1/2v  [Equation 6]
As illustrated in Equation 6, the receiving end relies on the value of
  ∑  k  2to restore the transmission signal s. Here, k=1, 2, . . . , N and N represents a number of transmission antennas. That is, because the value of
  ∑  k  2corresponds with the value of the SNR, having a large SNR means that the restoring capability of the signal is outstanding.
However, because the value of
  ∑  k  2includes the status of channels corresponding to all of the transmission antennas, the values of
  ∑  k  2cannot all be outstanding.
As an illustration of this point, assume that H is a 4×4 matrix. H can be represented according to the following equation.H=[H1H2H3H4]  [Equation 7]
In Equation 7, H is represented by four columns, and each column signifies a channel corresponding to transmission signal transmitted via a transmission antenna. If all four channels maintain orthogonal relationship with each other, there is no interference among signals transmitted via each antenna. However, in operation, it is difficult for each column to maintain orthogonality with each other column. As such, there exists interference among signals transmitted via each antenna. The rate of interference increases with a number of columns with respect to the rate of non-orthogonal relationship between each column. As discussed above, with the increase in interference, the value of
  ∑  k  2decreases, and the decreased
  ∑  k  2value is the reason for a small SNR, thus lowering the quality of the received signal.